Chapter 12 Managing a Sovereign Wealth Fund: A View from Practitioners (2024)

^{TABLE 12.1}

Real Returns Across U.S. Asset Classes, 1928–2008

Sources: Global Financial Data (www.globalfinancialdata.com); U.S. Federal Reserve (www.federal reserve.gov/); Shiller (www.econ.yale.edu~shiller/).

¹Continuously compounded rates of real returns over the period, annualized, in percent.

²Annualized standard deviations of monthly returns.

^{TABLE 12.2}

Real U.S. Equity Returns by Category, 1925–2008

Source: Renaissance Investment Management.

¹Continuously compounded rates of real returns over the period, annualized, in percent.

Equity Risk over the Economic Cycle

Although equities generally outperform bonds and ensure better capital protection over the long term, exceptions occur (Bernstein, 1996). Returns will vary over time and can do so in a consistent manner over the economic cycle. Investors may experience significant shifts in the risk-return relationship if, for example, they invest at the early stage of a recession phase or the early stage of an expansion phase (Table 12.3). In an early expansion phase, the more capital an investor puts at risk, the higher the return that might be expected over time. If the investment is made in an early recession phase, the correlation between risk and return turns negative and the more capital an investor puts at risk, the higher the loss that might be suffered.

Precise timing with respect to the economic cycle is not possible, but at any point an investor can know with some confidence which phase the economy is not in. When performing portfolio simulations and allocations, such phases can be excluded from the analysis and allocations chosen based on the reduced choice set.

The conclusion is that investing in equities only for the long run cannot protect an SWF from significant wealth destruction in the short run, particularly in recession phases. A large loss, even if only temporary, may not be bearable by the SWF.

Long-Term Drawdown Risk for Single Asset Class Investment Strategies

Maximum drawdown is a summary risk measure particularly suited to SWFs’ long horizons. A drawdown is the peak-to-trough loss that an investor would suffer if the investor invests at a maximum of the market and sells at the minimum, before the recovery. It captures the maximum loss that an investor could have experienced over the period. Over 80 years’ history for the United States, Table 12.4 shows that all asset classes have suffered extremely high drawdowns in real terms.

An investment in treasury bills, for instance, would have barely protected the capital over the whole period and would have incurred significant purchasing-power losses, almost 50 percent at a maximum. It took 45 years to recover the loss from the trough. The SWF investment model should search for alternatives that avoid large and prolonged purchasing-power losses. This chapter argues that this objective can be met by combining assets (multi-asset-class strategies) in such a way that the risk is reduced and the probability of large drawdowns is reduced, using either static allocation or dynamic allocation.

Distinction Between Strategic Utility and Financial Utility

An SWF pursues financial objectives that may translate into strategic objectives, either planned and mandated, such as the funding of pension schemes, or on a one-time basis, such as during an economic downturn. Strategic objectives may include equity investment in strategic sectors (politically mandated investment in sectors considered important for political reasons, such as energy or high technology), but they may also include a wealth transfer to the government budget to support social policies.

Strategic objectives may be pursued at the expense of financial objectives. To avoid potential conflicts, SWFs can split their activities, teams, and legal bodies to separate strategic from financial objectives. This separation can be facilitated and highlighted by the exercise of defining the utility function. The conceptual distinction between the two sets of objectives in the utility function aids in translating the distinction into practical structures and mandates.

One study (Bernstein, Lerner, and Schoar, 2009) examines the relationship between funds’ organizational structures and their private equity investments. The conclusion is that mixing strategic objectives with financial objectives leads to a higher likelihood of investing at home and to conflicts between financial targets and strategic objectives: “SWFs with external managers tend to invest in lower P/E industries, which see an increase in the P/E ratios in the year after the investment. By way of contrast, funds with politicians involved invest in higher P/E industries, which have a negative valuation change in the year after the investment” (Bernstein, Lerner, and Schoar, 2009, p. 28). The results of this study argue for a clear separation of the strategic and the financial parts of the SWF’s utility function.

Figure 12.4 shows a pro forma utility function for an SWF, separating the utility into strategic and financial components. Figure 12.5 concentrates on the financial component.

Mathematical Translation of the Financial Utility Function

The mathematical definition of a financial utility function requires a comprehensive understanding of both purchasing-power expectations and the cost of risk. The standard approach to portfolio optimization (mean-variance optimization) assumes utility depends on only the mean or expected return and the volatility of that return, as measured by its variance. This simple utility function is appropriate when either the distribution of returns is normal (in that case, the mean and variance completely describe the distribution) or investors actually care only about expected return and volatility.

For SWFs, such a utility function is generally too simplistic. The wealth component of utility must specify a target for purchasing power in the denominated currency. The cost or risk component of utility must be expanded; risk as a linear function of volatility may not be appropriate. First, risk measures such as VaR, expected shortfall, or drawdown risk may be included in addition to volatility. A normal distribution need not include VaR or expected shortfall because these measures will be simple functions (multiples) of volatility. In practice, distributions of returns have fat tails and VaR or expected shortfall will help measure the loss the fund can suffer without being forced to modify its investment philosophy. Second, liquidity measures may be included. These will depend on the amounts the fund could be requested to transfer to the strategic arm in the short term. Third, the unique funding position of SWFs—often from commodity revenues—means that correlations with particular asset classes may be specifically included.

The different components are blended into one utility function, written as

$\text{Utility = purchasing power}-\text{cost of risk.}$

This utility function can be used by portfolio managers to monitor asset allocation and risk parameters. The expected return function is based on assets’ yields and valuation models. The cost of risk function depends on the SWF’s risk metric and takes into account assets’ idiosyncratic risks, asset dependencies, and the SWF’s risk preferences.

Assets’ Idiosyncratic Risks

The P&L distribution of an asset incorporates all aspects of idiosyncratic risk, but it is generally convenient to concentrate on one or another risk measure that summarizes the variability of the distribution. Volatility (measured by standard deviation) is useful for its simplicity. In practice, there are additional risk measures that are as or more suitable:

• The tail of the P&L distribution, which is essentially a VaR measure but accounts for long periods and incorporates mean growth.

• Drawdown risk, which captures the possibility of serial correlation of losses leading to cumulated and prolonged diminution of wealth.

• Risk and return conditional on the economic and financial environment.

The traditional VaR measures the lower tail of the distribution. It is a loss threshold, with a certain probability of losing more than that threshold amount at the end of a period. The period is usually short and the VaR is usually calculated as a deviation from the mean or median. As argued above (see also Figure 12.2), the growth in the mean can be important for long-term investment and it is thus important to consider the distribution and the lower tail, including the mean growth.

Financial transactions exchange utilities between market participants, that is, expected trade-offs between return and risk as well as risk appetite. The interconnection between market participants creates positive feedback mechanisms that can lead to self-fulfilling prophesies, particularly for the demand for cash or its counterpart, the so-called market risk appetite. Such feedback mechanisms can create extended periods of good or bad results and produce, for low returns, persistent underperformance. The drawdown risk measure is intended to capture persistency, that is, to be sensitive to persistence and serial correlation in losses.

Figure 12.6 shows drawdown and evidence of persistence in returns for the S&P index. The horizontal axis represents drawdown in year t + 1, that is, the maximum peak-to-valley percentage return during the year t + 1. The vertical axis represents the frequency (probability) of that drawdown. Each of the four lines represents a specified level of drawdown in year t (for example, drawdown worse than 10 percent or drawdown worse than 20 percent). From Figure 12.6, we can see that the curves for higher drawdowns in year t are above the curves for lower drawdowns. This represents persistence: the probability of a severe drawdown in year t + 1 increases after a large drawdown in year t.

Asset Dependencies

Static Allocation

Static allocation means an allocation of assets that is not based on the present economic environment. Developing a static allocation involves analyzing asset risk and dependencies over a long period (over many business cycles)—including times of high and low inflation, high and low equity risk premiums, and various economic growth situations—and calculating the optimal allocation on the long-term efficient frontier.

The standard portfolio allocation process of modern portfolio theory involves the efficient frontier, plotting returns as a function of volatility, and choosing the best possible asset allocation over a period. The process can be extended to incorporate a measure of real drawdowns. We use genetic algorithm techniques that create random populations of portfolios and mutate them to mimic a Darwinian selection process. The utility function, or “fitness,” of any portfolio includes the portfolio return together with a cost of risk, counted negatively, for instance, the maximum drawdown multiplied by a scaling parameter.

The algorithm randomly generates a large number of candidate solutions (portfolios). Each portfolio is defined by its genes, that is, its allocations to the underlying assets. The best candidates survive; the worst ones are eliminated and replaced by a new population of survivors or “children” (resulting from a recombination of “parents’ genes” and from random mutations of genes). The process is repeated many times to converge toward an optimal or near-optimal set of solutions.

Genetic algorithms are nothing but optimization tools but with two major qualities:

• The fitness function can include a variety of risk components, such as moments, drawdowns, correlation to various indices, and so forth. This flexibility is particularly important for monitoring complex utility functions, as described in the section above titled Mathematical Translation of the Financial Utility Function.

• Genetic algorithms can explore a vast universe of solutions relatively quickly.

Static allocation is simple to implement and is a first step toward risk mitigation. The strategy does not, however, address the issue of model uncertainty and data (particularly correlation) instability. It can be quite rigid, particularly in times of crisis when asset correlations increase in tandem with market volatilities.

Among the most significant issues is that static allocation assumes that asset dependencies will be relatively stable, when in fact they can change for prolonged periods. Consider, as an example, the informal currency arrangements that have held during the decade since 2000: several countries have effectively fixed their currencies relative to the U.S. dollar (at undervalued levels according to many commentators) and funded the U.S. current account deficit. The behavior of all asset classes relative to the U.S. dollar has been distorted by this arrangement, altering dependencies relative to earlier periods. Another example is that in the decade to come, the increased risk of commodity shortages could alter the historical pattern of commodity dependencies versus traditional asset classes. For these and other reasons, dynamic allocation, considered next, is viewed as an essential alternative.

Dynamic Allocation

Dynamic allocation among various asset classes is a way to both extract value from asset price behavior in various economic regimes and to control risk exposures. It is the most sophisticated and controlled process for monitoring drawdown risks. Dynamic allocation is based on the observation that there are long-term regularities in asset returns based on the phase of the economic cycle. Figure 12.9, for example, shows that commodity prices tend to follow the economic cycle; that is, prices accelerate with the expansion phase and decelerate with the recession phase, while stock markets and bond markets tend to anticipate the economic cycle.

Diversification and dynamic rebalancing provide a first layer of protection against risk, both readily identifiable day-to-day risk, and tail-end risks that are largely unknown and unpredictable.

Principle I: Top-Down Macroeconomic Analysis

Top-down macroeconomic analysis acts as a filter to the investment universe. The objective is not to forecast the market but to try to avoid regional and global macro risks that can translate into sudden monetary outflows and the regional collapse of debt, equity, and currency markets. Regional imbalances can be gauged by measuring features such as external balances, debt levels and the currency denomination of the debt liquidity profile, and currency regime (e.g., fixed versus floating). Investing in economies with sound macroeconomic fundamentals is a first layer of protection against the erratic behavior of so-called hot money.

The second objective of macro research is to estimate the current position of the economic cycle. Economies exhibit a succession of booms and busts. Asset returns are particularly sensitive to two factors: price levels and economic cycles. Figure 12.10 shows the dispersion of S&P equity returns in four different market phases as a function of price levels, measured as the P/E ratio at the entry into the market phase. The figure shows that equities provide higher returns when P/Es are low in any market phase. Figure 12.10 also shows that equity rebounds usually happen during the late recession phase, well in advance of the economy as a whole.

Measuring the precise position of the economic cycle can be a difficult and uncertain exercise. However, a few conclusions can be drawn with a high degree of confidence. At any moment, an investor knows which one of the four phases the economy is not in. For example, at the time of this writing in early 2009, the U.S. economy may be in early recession or late recession, but it most certainly is not in a late expansion phase. When performing portfolio simulations, such historical phases can be excluded from the data set. The investor can also make reasonable assumptions about the relative likelihood of the remaining three phases. In the absence of satisfactory information, the investor can assign equal weight to the likelihood of each phase and stress test the portfolio in the three cases.

Principle II: Value Investing

Value investing across asset classes is a principle that improves the safety and mitigates the risk of a portfolio. Asset prices tend to oscillate around their fair values. A “cheap asset” has two advantages for a long-term investor: First, it offers higher yield, meaning the probability that it will deliver real value over time is high. Second, if the market moves adversely, a cheap asset is less likely than an expensive asset to be priced dramatically downward by the market, a situation that a long-term investor does not want to face.

The valuations of assets can be assessed with mathematical models. Although these models are imperfect, they are more robust for value investment than are market forecasts.

Figure 12.11 shows that investors usually overpay for the hope of growth. The earnings for equities classified as value investments turn out to be close to those predicted by analysts (actual is close to expected) and higher than in the prior period. In contrast, the earnings for equities classified as growth investments turn out to be lower than both predicted earnings and prior-period earnings. This shows that for growth companies analysts’ expectations for earnings seem to be based on priors, as if expectations were reverse engineered to match market price, and actual earnings disappoint relative to prior and expectations. For value companies the reverse is true, with the actual outcome close to expectations and higher than the prior.

Value concepts at the company level aggregate at the country or sector index levels and provide investment guidelines to enhance yield expectations across market phases.

For example, Table 12.6 shows the total return to the S&P 500 in different inflationary environments, and also for low versus high P/Es. Total returns are higher in low-inflation environments, but regardless of the circ*mstances, investing in equities when P/Es are low provides higher returns than when P/Es are high. Dynamic reallocation across asset classes based on value concepts is a process used for extracting value.

Although value investing focuses on yield, and therefore on expected returns, risk should not be ignored. Any market participant’s utility function combines expected return and risk. If asset prices tend to oscillate around their equilibrium value, so does the global appetite for risk, or its counterpart, the demand for cash.

The market’s risk appetite for a given asset or asset class can be measured in various ways, including by trend-following models using a medium-term time frame. The more favorable situation for a long-term investor occurs when risky assets are assigned a low price for embedded value while the market appetite for risk is growing. In 2009, analysts witnessed an example of this situation, in line with the historical behavior of equities and corporate bonds at the end of a recession phase and the beginning of an expansion phase.

Inclusion of the risk component in the asset-valuation process can also protect the portfolio from secular shifts in assets’ offer and demand equilibrium, which cannot be predicted using historical data. This issue is especially relevant for commodities, which do not bear interest and therefore cannot be easily integrated into a simple value-investing approach.

Principle III: Risk-Management Discipline

Risk-management discipline is an additional, critical layer of protection against tail-end risk. Asset managers make assumptions based on valuation methods and economic analysis, and those assumptions can turn out to be wrong. A crucial element of the investment process is to measure the consequences of being wrong and to ensure that such consequences would be bearable by the SWF owner.

Defining an SWF utility function is the process managers use to clarify the mandate entrusted to them. Risk-management discipline requires that the cost-of-risk function be monitored to ensure that the portfolio remains within its risk parameters.

Process

Global portfolio construction starts with mapping the investment universe and filtering that universe using top-down macroeconomic considerations. This first step leads to investment restrictions and constraints (i.e., particular geographic regions or asset classes to include or exclude) that are used during the portfolio optimization process.

The second step involves assessing individual asset valuations. Considerations of risk and return presented in the previous sections are implemented at this stage. In general, an asset’s value in a portfolio results from the trade-off between expected return and risk, as well as its correlation with other assets. The valuation and filtering process at this stage selects suitable assets, so that each investment, taken individually, provides a favorable expected risk-return trade-off. Prefiltering to choose suitable assets reduces the universe of assets considered in the third stage by the optimization routine, and enhances the robustness of the optimization process, which otherwise can be overly sensitive to the assumptions made in the correlation structure.

The third stage involves the fund’s utility function, which is used to optimize allocations to various assets under several constraints, such as liquidity requirements, macro restrictions on asset exposures, maximum tolerable volatility, or cost of transactions.

Back-Testing

Portfolio construction is a combination of science and art. The process requires the discretionary views of experienced managers in addition to computerized models to support the calculation process. It is not possible to look back in time and assume what discretionary decisions would have been made in the past. However, it is possible to build simplified models to simulate the actual process, and apply these models to past history. This exercise gives a reasonable semblance of the dynamics of the portfolio reallocation process and its potential strengths or weaknesses, at different time scales or under different economic regimes.

Such back-testing is essential, especially for measuring the potential consequences of being wrong. Managers and economists make mistakes all the time, and this is an intrinsic element of the investment process. The impact of making such mistakes can be examined by stress testing. For example, investing in equities in a late recession phase as opposed to in an early expansion phase has little consequence as measured by returns but significant costs in volatility. The control of the portfolio risk provided by a dynamic reallocation process offers some element of comfort with regard to economic uncertainties.

Managing Tail Event Risk